Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation e^x=0
-
Equation x^2=10
-
Equation cos(x)=3
-
Equation x^2-3x-4=0
- Express {x} in terms of y where:
- 2*x+2*y=-6
- 7*x+20*y=-17
- 12*x+14*y=-15
- -11*x+10*y=-9
- Derivative of:
-
sin(x)
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3/4
- Integral of d{x}:
-
sin(x)
- Canonical form:
- sin(x)
- Sum of series:
-
3/4
- Limit of the function:
-
3/4
-
Identical expressions
- sin(x)= three / four
- sinus of (x) equally 3 divide by 4
- sinus of (x) equally three divide by four
- sinx=3/4
- sin(x)=3 divide by 4
-
Similar expressions
- sinx=3/4
sin(x)=3/4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{3}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} = \frac{3}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi - asin(3/4) + asin(3/4)
$$\operatorname{asin}{\left(\frac{3}{4} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{3}{4} \right)}\right)$$
=
pi
$$\pi$$
product
(pi - asin(3/4))*asin(3/4)
$$\left(\pi - \operatorname{asin}{\left(\frac{3}{4} \right)}\right) \operatorname{asin}{\left(\frac{3}{4} \right)}$$
=
(pi - asin(3/4))*asin(3/4)
$$\left(\pi - \operatorname{asin}{\left(\frac{3}{4} \right)}\right) \operatorname{asin}{\left(\frac{3}{4} \right)}$$
(pi - asin(3/4))*asin(3/4)
Rapid solution
[src]
x1 = pi - asin(3/4)
$$x_{1} = \pi - \operatorname{asin}{\left(\frac{3}{4} \right)}$$
x2 = asin(3/4)
$$x_{2} = \operatorname{asin}{\left(\frac{3}{4} \right)}$$
x2 = asin(3/4)
Numerical answer
[src]
x1 = 2.29353057460831
x2 = -30.5678644569164
x3 = -98.2374343402651
x4 = -54.255137190008
x5 = -1606.20190806337
x6 = 13.4144326933407
x7 = -43.1342350712756
x8 = 71.4085689535838
x9 = -3.98965473257127
x10 = 82.5294710723161
x11 = 52.559013032045
x12 = -55.7006056856348
x13 = 76.2462857651365
x14 = -124.81564406461
x15 = -66.8215078043671
x16 = -35.4055812684692
x17 = -3792.75039496186
x18 = 0.848062078981481
x19 = 21.1430864961471
x20 = -36.851049764096
x21 = -87.1165322215327
x22 = -60.5383224971876
x23 = -148.502916797702
x24 = 19.6976180005202
x25 = -24.2846791497369
x26 = -2279.94820442721
x27 = 101.379026993855
x28 = 95.0958416866753
x29 = -22.83921065411
x30 = 272.470498783331
x31 = 32.2639886148794
x32 = 17010.8761571097
x33 = -99.6829028358919
x34 = 14.8599011889675
x35 = 83.9749395679429
x36 = -41.6887665756488
x37 = -49.4174203784552
x38 = 58.8421983392246
x39 = -18.0014938425573
x40 = -61.9837909928144
x41 = 27.4262718033267
x42 = 51.1135445364182
x43 = 96.5413101823021
x44 = -91.9542490330855
x45 = 69.9631004579569
x46 = 38.547173922059
x47 = -29.1223959612896
x48 = 46.2758277248654
x49 = 33.7094571105062
x50 = -11.7183085353777
x51 = 90.2581248751225
x52 = -16.5560253469304
x53 = 63.6799151507773
x54 = -85.6710637259059
x55 = -47.9719518828284
x56 = 57.3967298435978
x57 = 25.9808033076998
x58 = 7.13124738616107
x59 = 7202.82389260241
x60 = -80.8333469143531
x61 = -68.266976299994
x62 = -74.5501616071735
x63 = -73.1046931115467
x64 = -10.2728400397509
x65 = -5.43512322819811
x66 = 44.8303592292386
x67 = -79.3878784187263
x68 = 8.5767158817879
x69 = -462.662182156681
x70 = 164.210880065651
x71 = 88.8126563794957
x72 = 65.1253836464042
x73 = 77.6917542607633
x74 = -93.3997175287123
x75 = 39.9926424176858
x75 = 39.9926424176858
The graph